Example.
There is a ball in the box. This ball may be black or white.
The probability to take a white ball is \(\frac1{2}\), because the probability of it to be a black ball is \(\frac12\).
But when there is a condition that you know it is black, the probability to take a white ball equals \(0\). That is called the conditional probability.
There is a formula for it:
\(P(A|B)=\frac{P(A\bigcap B)}{P(B)}\)

It is a definition of the conditional probability. It cant be proved.
There is a formula for the probability of the two independent events \(A,B\) happen at the same time:
\(P(A\bigcap B)=P(A)P(B)\)
From this, if \(P(B)\ne0\), you can divide this by \(P(B)\) and get the formula. I wish you think about this interesting question by yourself. If you do so you will understand it deeper.